Can you find the value of \(f'(20\pi)\)?

Calculus Level 3

Let \(f(x)\) be a function defined for all \(x\in\mathbb{R}\) such that \(f(x+y)=f(x)\cdot f(y)\) for all \(x,y\in\mathbb{R}\). Let \(f'(0)=18\) and \(f(20\pi)=\tfrac12\). What is the value of \(f'(20\pi)\)?

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